Quasi-stationary Process Research Articles

Exact analytical solution of the equations for a quasiequilibrium two-phase domain: permeability and interdendritic spacing

This study is concerned with the theoretical description of a quasi-stationary process of directional crystallization of binary melts and solutions in the presence of a quasi-equilibrium two-phase region. The quasi-equilibrium process is ensured by the fact that the system supercooling is almost completely compensated by heat released during the phase transformation. Quasi-stationarity of the process determining constancy of the crystallization rate is ensured by given temperature gradients in the solid and liquid phases. The system of heat and mass transfer equations and boundary conditions to them under these assumptions is dependent on a single spatial variable in the reference frame moving with the crystallization rate relative to a laboratory coordinate system. Exact analytical solutions to the formulated problem in parametric form are obtained. The parameter of the solution is the solid phase fraction in a two-phase region. The distributions of temperature and impurity concentration in the solid, liquid and two-phase regions of the crystallizing system, the rate of solidification, and the spatial coordinate in the two-phase region depending on the solid phase fraction in it are found. An algebraic equation for the solid phase fraction at the interface between the solid material and the two-phase region is derived. Exact analytical solutions show that the impurity concentration in the two-phase layer increases as the solid phase fraction increases. Moreover, the solid phase fraction at the interface solid phase — two phase region and its thickness increase as the temperature gradient in the solid phase and the solidification rate increase. The developed theory allows us to determine analytically the permeability of the two-phase region and a characteristic interdendritic spacing in it. Analytical solutions show that the relative permeability in the two-phase region increases from a certain value at the interface with the solid phase to unity at the interface with the liquid phase. The selection theory of stable dendritic growth allows us to determine analytically a characteristic interdendritic distance in the two-phase layer that decreases as the temperature gradient in the solid phase increases. An increase of impurity in the molten phase gives a decrease in the interdendritic spacing within a two-phase region.

Evaluation of the Limitation of Operational Parameters of the IEEE 802.11 ac Network in the 20MHz Channel

IEEE 802.11 wireless network technologies are widely used to create corporate and personal local networks for data exchange and access to Internet resources. The main principle of operation of IEEE 802.11 networks is the principle of competitive access, according to which all wireless network users have the same access rights to the information transmission environment. This method of access leads to the occurrence of collisions in networks with a large number of users, which complicates the process of network functioning and leads to the degradation of quality indicators. The purpose of the study is to estimate the limit values of the operational characteristics of the IEEE 802.11 ac wireless network in the mode with the highest transmission rate (MCS8) in a frequency channel of 20 MHz with one spatial stream, provided that the network has a significant number of active stations with a saturated load. An alternative model of processes in IEEE 802.11 networks based on the concept of a virtual competitive window is used for research. According to the concept of virtual contention window (VCW), the process of data transmission in a network with competitive access is considered as a quasi-stationary process. Numerical data were obtained and graphs of channel bandwidth, transmission delay, and delay non-uniformity were given in the presence of one to sixteen active stations with a saturated load in the network, in the case of transmission of frames with a data volume of 512 or 1500 bytes. The maximum possible bandwidth of the channel with a frequency band of 20 MHz (68.387 bit/s) was determined, in the case of using frames with the maximum load (11454 bytes) provided by the standard. Estimated data on the number of collisions occurring in a network with a saturated load and the number of frames transmitted at various stages of channel access are also provided. The frame transmission delay increases almost proportionally to the number of active stations and varies from 0.605 ms to 5.293 ms, in the case of loading all data frames of 512 bytes, and from 0.785 to 6.41 ms, in the case of a load of 1500 bytes, for changes in the number of active stations in the network from 2 to 16. The unevenness of the delay exceeds the average delay and grows non-linearly, in the case of an increase in the number of active stations from 1 to 6 (CWmin=15), and linearly — with a further increase in the number of stations (over 6). The obtained results are useful for reasonable planning of wireless networks and configuration of network equipment parameters.

Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes

Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Loève spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Loève spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Loève spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Loève spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023.

Methodology for Determining Heat Losses through Translucent Construction

The purpose of this work is to determine the heat transfer coefficient of translucent fences, considering the number of storeys of buildings, climatic factors, such as wind velocity and outdoor temperature. To achieve this goal, the following tasks were solved: analysis of heat transfer in translucent enclosures as a quasi-stationary process; analysis of heat transfer processes in translucent barriers, which are a combination of solid transparent plates and air gaps connected by a frame structure; determination of the heat transfer coefficient on the glass surface depending on climatic factors and the radiant component. The most important result is the empirical dependence of the heat transfer coefficient on the outer surface of the window block on the Reynolds criterion, the dependences for determining the heat transfer coefficient of window blocks are improved, considering climatic parameters. The heat transfer coefficient of the window block as a whole is presented in the form of analytical ratios, considering the location of the building and its height, changes in wind velocity and outdoor temperature. This methodology was tested on the example of a civil administrative building, for which the heat transfer coefficients of window structures of non-standard series were evaluated. The significance of the research results lies in the possibility of using the obtained dependencies to assess the thermal characteristics of window structures of non-standard shapes. The dependences of the heat transfer coefficient on wind speed and outside air temperature given in the paper can be used in the energy audit of buildings.

Refined Spatio-Temporal Model of Accelerations of the Main Geomagnetic Field on the Earth’s Surface and Geomagnetic Jerks

Refined spatial spherical harmonic models of the piecewise constant field of secular geomagneticaccelerations have been constructed based on the concept of geomagnetic jerks. The data of the 189 magneticobservatories operating during the extended period of investigations have been analyzed, assuming that jerksare manifestation of sharp changes in regimes of quasi-stationary magnetohydrodynamic process of generationof geomagnetic secular variations in the high-frequency spectrum range. Qualitative and quantitativeanalyses have been carried out, showing the persistency of models of the current generation, and their consistencywith the acceleration field values obtained from direct observatory observations data. The epochs ofjerks that occurred in the extended time period were refined and it was found that on the global scale theyhave quasi-decadal repeatability, through which it is possible to estimate the time characteristics of regimesof the stationary evolution of the magnetic field of the Earth’s core. An analysis of the results of spherical harmonicmodeling using the maps of the global field of accelerations showed that the origins of all identifiedjerks are of an intraterrestrial character, which also provide the specific features of their morphological structure,as well as the degree of their distribution on the Earth’s surface

MATHEMATICAL MODELING OF THE QUASI-STATIONARY PROCESSES OF VISCOUS MIXTURE MIXING IN A RECTANGULAR AREA BY THE R-FUNCTIONS METHOD

Mixing processes are found in the chemical, pharmaceutical and food industries. Fluid mixing is one of the fundamental scientific problems associated with modern concepts of regular and chaotic dynamics. The paper considers the problem of mathematical modeling of the quasi-stationary process of mixing a viscous mixture. This problem consists of two sub-problems: determination of the velocity field in the flow region (Eulerian formalism) and investigation of the trajectories of individual fluid particles (Lagrange formalism). To solve the first subproblem, it is proposed to jointly use the principle of superposition, the structural method (method of R-functions) and the Ritz variational method. The methods of nonlinear dynamics and qualitative theory of differential equations are used to solve the second subproblem. A plane quasi-steady flow is considered in a rectangular region and it is assumed that the side walls are at rest, and the upper and lower walls move alternately according to the given laws. According to the method of R-functions, the structures of the solutions were built and the use of the Ritz variational method for the approximation of the uncertain components of the structures was justified. The operation of the proposed method is illustrated by the results of a computational experiment, which was conducted for different modes of wall motion. The practical interest of the considered regimes is due to the fact that they lead to the emergence of chaotic behavior when mixing occurs most efficiently. Using the methods of nonlinear dynamics, the location of periodic (hyperbolic and elliptical) points was investigated and the Poincaré section was constructed. Further research with the help of the method proposed in the work can be related to the consideration of flows in more geometrically complex regions and more complex mixing regimes, as well as in the application to the calculation of industrial problems.

Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity

Although the entropy of black holes in any diffeomorphism invariant theory of gravity can be expressed as the Wald entropy, the issue of whether the entropy always obeys the second law of black hole thermodynamics remains open. Since the nonminimal coupling interaction between gravity and the electromagnetic field in the general quadric corrected Einstein-Maxwell gravity can sufficiently influence the expression of the Wald entropy, we check whether the Wald entropy of black holes in the quadric corrected gravity still satisfies the second law. A quasistationary accreting process of black holes is first considered, which describes that black holes are perturbed by matter fields and eventually settle down to a stationary state. Two assumptions that the matter fields should obey the null energy condition and that a regular bifurcation surface exists on the background spacetime are further proposed. According to the two assumptions and the Raychaudhuri equation, we demonstrate that the Wald entropy monotonically increases along the future event horizon under the linear order approximation of the perturbation. This result indicates that the Wald entropy of black holes in the quadric corrected gravity strictly obeys the linearized second law of thermodynamics.

Adaptive Algorithm of Quasi-Stationary Periodic Processes Measurements Control

The aim of the work was to create an effective method of control of linear measuring systems functioning in the conditions of the prevailing influence of distortions caused by variability in time of measuring conversion parameters. The method and the algorithm of control of measurements of the quasi-stationary periodic process spectrum in frequency-domain and form in time-domain are presented, consisting in the simultaneous separate observation of the parameters of the process under probe and the parameters of the measuring system with the subsequent introduction of corrections. The control of system parameters is carried out using the artificial stationary polyharmonic sample impact. The spectra of the main and sample processes are not intersected. A synthesizing method of the form in time-domain of the sample impact process is presented. The main limitations and the range of conditions for the possible application of the method are determined, its effectiveness is shown on the example of the experimental data obtained during the low-frequency inductive electrical prospecting system functioning in alternating magnetic field measuring mode.

Reactor for Waste Gasification with Highly Superheated Steam

Using highly superheated steam (HSS) with a temperature of above 2000 K for oxygen-free gasification/detoxification of industrial, municipal, and toxic waste, the organic component of waste can be completely converted to syngas or power gas. It was proposed for the first time to produce such HSS by cyclic detonation of stoichiometric ternary mixtures fuel–oxygen–steam at a near-atmospheric initial pressure and to feed it into a cooled flow-type spherical reactor as supersonic countercurrent two-phase jets together with finely divided waste particles. Three-dimensional gas-dynamic calculations showed that the cyclic feed of supersonic jets into the reactor gives rise to intense vortex zones of high-temperature HSS. Waste particles repeatedly enter into these vortex zones and are gasified or heat-treated, and the shock waves accompanying the feed of the supersonic jets prevent particle agglomeration. In the quasi-stationary operation process, a small overpressure is maintained in the reactor (to prevent the suction of atmospheric air), and the median mean residence time of the particles is sufficient for their complete gasification.

Improvement of a single-phase rectifier for manual arc welding by stick electrode for thin-sheet constructions

The article shows the results of work to improve the single-phase rectifier for manual arc welding of thin-sheet structures. An additional unit is proposed, which is an electronic switch that includes a control circuit for the rectifier thyristors for two half-periods with a constant frequency, a multiple of the number of half-periods of the rectified current. At the same time, the selection of mode parameters for manual arc welding with a coated electrode allows for a stable quasistationary process of melting and transfer of the electrode metal. The use of an additional unit provides welding thin-sheet structures without reducing the diameter of the coated electrode, by analogy with the known processes for welding in protective gas.

Approximations and forecasting quasi-stationary processes with sudden runs

The object of research is heteroskedastic processes in the formation and evaluation of the offset policy of states in international markets, in particular, in the conclusion and execution of offset contracts. The process of concluding and fulfilling the conditions of an offset contract is weakly unsteady, because at its conclusion there can be a wide variety of sudden events, force majeure circumstances that can’t be described and predicted in detail, with acceptable accuracy, in full. It is shown that the term «quasi-stationary process», which has some approximation to the stationary process, is more suitable for describing such processes. The most promising approach to constructing mathematical models of such processes is the use of combined fractal autoregression models and an integrated moving average. During the study, methods of the theory of non-stationary random processes and the theory of runs of random processes were used, it is shown that the combination of a quasi-stationary process with a sequence of random runs is quite satisfactorily modeled by the so-called fractal or self-similar process. As a universal mathematical model of self-similar processes with slowly decreasing dependencies, the model of fractal integrated autoregression and the moving average FARIMA are used. However, this model does not take into account the effect of runs of random processes on the coefficients of the numerator and denominator of the finely rational function, which approximates the process of autoregression and the moving average. Therefore, in the study, the relationship in the parameters of the runs and the coefficients of the approximating function. Mathematical models of discrete time series are considered, which are characterized by quasi-stationary and the presence of sudden runs. It is shown that for approximation of such series, models such as autoregression and moving average are quite suitable, modified to the classes of autoregression models and integrated moving average. And for self-similar (fractal) processes – modified to the classes of models of autoregression and fractal integrated moving average. The relationship between the shear length when calculating autocorrelation coefficients and the total sample length can serve as an acceptable indicator of the correctness of the solution.

The Statistical Characteristics and Calculated Values for Air Temperature in Building`S Cladding Design

The article demonstrates the methodology and the results of statistical characteristics determination and territorial distribution as well as free air winter temperature calculated values required for the designing the building`s cladding.Daily temperatures of free air have been described by a probabilistic model of quasi-stationary differentiable random process. The expectation function is set by the Fourier series or sequence of monthly temperatures, the standard and asymmetry are determined by the mathematical expectation. The Ordinates Distribution Law is described by a linear combination of Gauss and Gumbel distributions. The frequency structure is determined by the time-constant value of the effective frequency. The required statistical characteristics are determined by the results of systematic measurements of average daily air temperature at 485 observation points inUkraine.The calculated values of winter air temperature are determined by using probabilistic approach with accounting for return period equal to building working life, as well as temperature averaging interval, reflecting building`s cladding thermal inertia. The map of territorial distribution of Ukraine has been created based on free air temperature values and dependencies which can lead to calculated values taking into account given building operating life, temperature averaging interval and altitude in mountainous regions.The developed methodology ensures the possibility of minimal calculated values determination for free air temperatures including all the factors mentioned above, and the suggestions as for introduction of norms enabling accounting for building`s cladding thermal inertia within the building working life when making thermotechnical characteristics calculations.

VIBRATION PIERCING OF PIPE BILLET ON THE PIERCING PRESS OF PIPE-ROLLING MILL

The issues of using highly efficient technologies in the production of pipes on the piercing press of a pipe press installation are considered. The existing basic and perspective directions of intensification of deformation modes in the processes of metal forming using active controlled high-frequency vibrations are analyzed. It was established that, due to insufficient study, vibration processes do not find wide application in the production of seamless pipes. By analyzing and synthesizing a number of known fundamental studies, it has been shown that favorable conditions for metal deformation can be achieved by using high-frequency vibrations. It was revealed that the operation of the pipe billet piercing on the piercing press is accompanied by considerable losses to overcome the forces of technological resistance, characteristic for the process of deformations unevenness throughout the volume of the processed metal. Some previously unknown phenomena that arise during the implementation of existing technologies for pipe billets piercing have been established, which required the creation of new mathematical models of such processes that adequately reflect the conditions of the process of piercing or expanding the billets on modern piercing presses. A mathematical model of the dynamic wave processes arising in the processed metal is made. For the quasistationary process of pipe billet piercing differential equations of wave formation are obtained at the corresponding boundaries of the zones of the deformation center, characteristic for the plastic zone and the zone with cracking in the pierced metal. The parameters of the wave propagation boundary in the pierced pipe billet on the conjugate fronts of the plastic zone with the zone of crack formation are determined. It was established that deformations and stresses in the pierced metal depend on the rate of expansion of characteristic waves at the interface of contact with technological tools. A highly effective innovative technology of vibration piercing of a pipe billet on a piercing press of a pipe-rolling mill is substantiated. The features of realizing the technology of active controlled vibration piercing of the pipe billet on the piercing press of a pipe-rolling mill are determined. It is shown that the use of high-frequency oscillations on the press contributes to a significant increase in the efficiency of the technological process of piercing or expansion of pipe billets. The choice of rational parameters of high-frequency vibrators (amplitude-frequency characteristics), built into the system, resulted in a noticeable decrease in the energy-strength parameters du­ ring the piercing of the pipe billet and a significant improvement in the quality of the produced sleeves.

A theory of self-organized zonal flow with fine radial structure in tokamak

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters; the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process, the cycle of ITG wave energy is composed of two consecutive phases in distinct spatiotemporal structures: a pair of Cavitons growing and breathing slowly without long range propagation, followed by a sudden decay into many Instantons that carry negative wave energy rapidly into infinity. A spotlight onto the motion of Instantons for a given radial position reproduces a Blob-Hole temporal structure; the occurrence as well as the rapid decay of Caviton into Instantons is triggered by zero-crossing of radial group velocity. A sample of the radial profile of zonal flow contributed from 31 nonlinearly coupled rational surfaces near plasma edge is found to be very similar to that observed in the JET Ohmic phase [J. C. Hillesheim et al., Phys. Rev. Lett. 116, 165002 (2016)]. The theory predicts an interior asymmetric dipole structure associated with the zonal flow that is driven by the gradients of ITG turbulence intensity.

Effect of frequency on natural convection flows induced by a pulsating line-heat source

Laminar natural convection around a thin platinum wire immersed in a large pool of liquid water and submitted to a pulsating heat flux is investigated. First is presented an analytical model aiming at predicting time-evolution of the wire temperature as a function of the frequency. The major assumption consists in modelling heat transfer between the wire and the fluid by a heat transfer coefficient, of constant value. Experiments and numerical simulations are performed. Oscillations of the wire temperature are first investigated comparing the analytical approximation with the experimental and numerical results. The amplitude is reduced as the frequency increases and the phase-shift increases. At low frequency, a quasi-stationary process is observed. At high frequency, the amplitude tends to zero while the phase shift tends to a limit equal to −45°. Numerical simulations reveal that similar trends are observed for the amplitude of the temperature signals recorded in the fluid at various locations in the symmetry line above the wire. This amplitude is estimated for these locations as a function of the frequency using a 1D unsteady convection-diffusion equation to model heat transfer in the fluid. Heat diffusion associated with the initial non uniform temperature field is seen to be a major effect at short distance, i.e. less a few times the characteristic dimension of the wire. Advection induced by the initial velocity distribution dominates in the far-field, i.e. for a distance greater than about ten times the characteristic dimension of the wire.

Nonlinear model of quasi-stationary process in crystalline semiconductor

Nonlinear model of quasi-stationary process in crystalline semiconductor

Mixed-mode oscillations in a nonlinear time delay oscillator with time varying parameters

In this study, the mechanism for the action of time-invariant delay on a non-autonomous system with slow parametric excitation is investigated. The complex mix-mode oscillations (MMOs) are presented when the parametric excitation item slowly passes through critical bifurcation values of this nonlinear time delay oscillator. We use bifurcation theory to clarify certain generation mechanism related to three complex spiking formations, i.e., ``symmetric sup-pitchfork bifurcation'', ``symmetric sup-pitchfork/sup-Hopf bifurcation'', and ``symmetric sup-pitchfork/sup-Hopf/homoclinic orbit bifurcation''. Such bifurcation behaviors result in various hysteresis loops between the spiking attractor and the quasi-stationary process, which are responsible for the generation of MMOs. We further identify that the occurrence and evolution of such complex MMOs depend on the magnitude of the delay. Specifically, with the increase of time delay, the two limit cycles bifurcated from Hopf bifurcations may merge into an enlarged cycle, which is caused by a saddle homoclinic orbit bifurcation. We can conclude that time delay plays a vital role in the generation of MMOs. Our findings enrich the routes to spiking process and deepen the understanding of MMOs in time delay systems.

ТЕОРЕТИЧЕСКИЙ АНАЛИТИЧЕСКИЙ МЕТОД РЕШЕНИЯ ЗАДАЧИ ПРОЦЕССА ВАКУУМНОГО ЗАМОРАЖИВАНИЯ ЖИДКОСТИ В СПОКОЙНОМ СОСТОЯНИИ

A generalized closed analytical solution of the problem of a quasi-stationary process in liquid vacuum freezing in a quiet state with regard to the thickness of the frosting layer ξ whereas heretofore numerical solutions of this problem occurred. The advantage of the analytical solutions obtained of the problem of a quasi-stationary vacuum freezing of moisture in a finedispersion state over existing numerical ones consists in the identification of an immanent tie between defining and determined parameters regarding a thickness of the frosting layer ξ. It is also possible to use them directly at the computation without resorting to the help of computers.

Model of Draining of the Blast Furnace Hearth with an Impermeable Zone

Due to demands of lower costs and higher productivity in the steel industry, the volume of operating blast furnaces has grown during the last decades. As the height is limited by the allowable pressure drop, the hearth diameter has grown considerably and, along with this, also draining-related problems. In this paper a mathematical model is developed for simulating the drainage in the case where an impermeable region exists in the blast furnace hearth. The model describes the quasi-stationary drainage process of a hearth with two operating tapholes, where the communication between the two pools of molten slag and iron can be controlled by parameterized expressions. The model also considers the case where the buoyancy of the liquids is sufficient for lifting the coke bed. The implications of different size of the liquid pools, communication between the pools, bed porosity, etc. are studied by simulation, and conclusions concerning their effect on the drainage behavior and evolution of the liquid levels in the hearth are drawn. The simulated liquid levels are finally demonstrated to give rise to a pressure profile acting on the hearth which agrees qualitatively with signals from strain gauges mounted in the hearth wall of an industrial ironmaking process.

Coarsening Mechanism for Systems Governed by the Cahn--Hilliard Equation with Degenerate Diffusion Mobility

We study a Cahn--Hilliard equation with a diffusion mobility that is degenerate in both phases and a double-well potential that is continuously differentiable. Using asymptotic analysis, we show that the interface separating the two phases does not move in the $t=O(1)$ or $O(\varepsilon^{-1})$ time scales, although in the latter regime there is a nontrivial porous medium diffusion process in both phases. Interface motion occurs in the $t=O(\varepsilon^{-2})$ time scale and is determined by quasi-stationary porous medium diffusion processes in both bulk phases, together with a surface diffusion process along the interface itself. In addition, in off-critical systems where one phase---the minor phase---occupies only a small fraction of the system and consists of many disjoint components, it is the quasi-stationary porous medium diffusion process that provides communications between the disjoint components and accounts for the occurrence of coarsening.